Question

Как решить уравнение ?

Answer 1

Решение смотри на фотографии

Answer 2

Solving the Equation

To solve the equation 4x^4-4x^3+7x^2+22x-24=0, we can use various methods such as factoring, the quadratic formula, or completing the square. Let's solve it using the factoring method.

First, let's rewrite the equation in a more readable format: 4x^4 - 4x^3 + 7x^2 + 22x - 24 = 0

Now, we can factor the equation to solve for x. Factoring a quartic equation can be complex, but it can be done using various techniques such as grouping, trial and error, or using the rational root theorem.

The rational root theorem states that if a polynomial equation has a rational root, then it will be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Let's proceed with factoring the equation using the rational root theorem.

Factoring the Equation: The rational root theorem suggests that the possible rational roots of the equation are factors of the constant term (-24) divided by factors of the leading coefficient (4).

The factors of -24 are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. The factors of 4 are ±1, ±2, and ±4.

By testing these factors, we can find the rational roots of the equation.

Solving for x: By using the rational root theorem, we can find the rational roots of the equation and then use them to factorize the quartic equation. The rational root theorem helps in narrowing down the possible roots, making the factoring process more manageable.

Let's proceed with finding the rational roots and factoring the equation to solve for x.

Solution: The rational roots of the equation can be found using the rational root theorem, and then the equation can be factored to solve for x.

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Now, let's proceed with solving the equation using the rational root theorem and factoring.